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{{About|the predator-prey equations|the competition equations|Competitive Lotka–Volterra equations}}

{{About|the predator-prey equations|the competition equations|Competitive Lotka–Volterra equations}}

{{short description|Pair of equations modelling predator-prey cycles in biology}}

{{short description|Pair of equations modelling predator-prey cycles in biology}}

[[File:Milliers fourrures vendues en environ 90 ans odum 1953 en.jpg|upright=1.5|thumb|Numbers of [[Lepus americanus|snowshoe hare]] (yellow, background) and [[Canada lynx]] (black line, foreground) furs sold to the [[Hudson's Bay Company]]. Canada lynxes eat snowshoe hares.]]

[[文件:Milliers fourrures vendues en environ 90 ans odum 1953 en.jpg|缩略图|右|卖给哈德逊湾公司的雪鞋野兔毛皮（后方黄色区域）和加拿大山猫毛皮（前方黑色线条）。注意：加拿大山猫吃雪兔。]]

 

snowshoe hare (yellow, background) and Canada lynx (black line, foreground) furs sold to the Hudson's Bay Company. Canada lynxes eat snowshoe hares.]]

 

雪鞋兔(黄色，背景)和加拿大猞猁(黑线，前景)毛皮出售给哈德逊湾公司。加拿大猞猁吃雪鞋兔[]

The '''Lotka–Volterra equations''', also known as the '''predator–prey equations''', are a pair of first-order [[nonlinear]] [[differential equation]]s, frequently used to describe the [[dynamical system|dynamics]] of [[Systems biology|biological systems]] in which two species interact, one as a [[predator]] and the other as prey. The populations change through time according to the pair of equations:

The '''Lotka–Volterra equations''', also known as the '''predator–prey equations''', are a pair of first-order [[nonlinear]] [[differential equation]]s, frequently used to describe the [[dynamical system|dynamics]] of [[Systems biology|biological systems]] in which two species interact, one as a [[predator]] and the other as prey. The populations change through time according to the pair of equations: